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Nature of Roots

Find the valu...

Question

Find the value of $m$ such that roots of the quadratic equation $x^{2} - (m - 3) x + m = 0$ $(m \in R)$ are equal.

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Solution

The correct option is B 1
Condition for equal roots :
$D = 0$
$\Rightarrow (m - 3)^{2} - 4 m = 0$
$\Rightarrow m^{2} - 6 m + 9 - 4 m = 0$
$\Rightarrow m^{2} - 10 m + 9 = 0$
$\Rightarrow (m - 1) (m - 9) = 0$
Either $(m - 1) = 0$ or $(m - 9) = 0$

Hence, $m = 1$ or $m = 9$

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